Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#358 ⋊ C2 |
| Sylow | C3 ⋊ #33527 |
1098 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|b^2=h,d^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,i^a=i^2,e^b=eg,g^b=gh,i^b=i^2,d^c=dh,i^c=i^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323448);